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Stochastic resonance in noisy maps as dynamical threshold-crossing systems

Matyjaskiewicz¹, Holyst, Krawiecki

¹Faculty of Physics, Warsaw University of Technology, Poland. matyjas@if.pw.edu.pl

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

|October 14, 2000

Summary

Stochastic resonance is observed in both the logistic map and the kicked spin model when noise and periodic modulation interact. This phenomenon indicates enhanced signal-to-noise ratio due to transitions between symmetric states.

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Area of Science:

Nonlinear Dynamics
Statistical Physics
Complex Systems

Background:

Investigates the interplay between noise and periodic modulation in dynamical systems.
Focuses on the logistic map beyond the first bifurcation and the kicked spin model with Ising anisotropy and damping.

Purpose of the Study:

To analyze the occurrence of stochastic resonance in two distinct complex systems.
To understand how periodic modulation affects transition probabilities between symmetric states.

Main Methods:

Theoretical analysis using adiabatic theory.
Numerical simulations to validate analytical results.
Examination of system dynamics under combined noise and periodic forcing.

Main Results:

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Both models exhibit two distinct symmetric states corresponding to different phases or attractors.
Periodic modulation symmetrically influences transition probabilities between states.
Stochastic resonance is observed in both systems, characterized by an optimal signal-to-noise ratio.

Conclusions:

The logistic map and kicked spin model behave as threshold-crossing systems with internal dynamics.
Stochastic resonance is a robust phenomenon in these systems, driven by noise and periodic modulation.
Adiabatic theory provides a qualitatively accurate framework for understanding these dynamics.